Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;


public class B {

	void run() {
		int n = in.nextInt();
		int m = (n+2)/2;
		out.println(m);
		for(int i = 1; i<= n;i++){
			int row = 1;
			int col = i;
			if(col > m){
				row += col - m;
				col = m;
			}
			out.println("" + row + " " + col);
		}
	}
	
	static MyScanner in;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		boolean stdStream = true;
		if(stdStream){
			in = new MyScanner();
			out = new PrintWriter(System.out);
		}else{
			String fileName = B.class.getSimpleName();
			int n_test = 1;			
			String inputFileName = fileName + String.format(".%02d", n_test) + ".inp";
			String outputFileName = fileName + String.format(".%02d", n_test) + ".out";
			in = new MyScanner(new BufferedReader(new FileReader(inputFileName)));
			out = new PrintWriter(outputFileName);
		}
			
		new B().run();

		in.close();
		out.close();
	}

	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

        MyScanner(){
            this.br = new BufferedReader(new InputStreamReader(System.in));
        }

		MyScanner(BufferedReader br) {
			this.br = br;
        }

        void close() throws IOException {
            br.close();
        }
        
		void findToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}
		
		String next() {
			findToken();
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}